In the last decade or so, the lattice Boltzmann (LB) method has emerged as a new and effective numerical technique of computational fluid dynamics (CFD).(1-5) Modeling of the incompressible Navier-Stokes equation is among many of its wide applications. Indeed, the lattice Boltzmann equation (LBE) was first proposed to simulate the incompressible NavierStokes equations.(1) The incompressible Nav...

This article gives an overview of the diverse range of teaching applications that can be realized using an interactive lattice Boltzmann simulation tool in fluid mechanics instruction and outreach. In an inquiry-based learning framework, examples are given of learning scenarios that address instruction on scientific results, scientific methods or the scientific process at varying levels of stud...

In this paper, we theoretically prove a set of fundamental conditions pertaining discrete velocity sets and corresponding weights. These conditions provide sufficient conditions for a priori formulation of lattice Boltzmann models that automatically admit correct hydrodynamic moments up to any given N-th order.

Intrinsic fluctuations around the solution of the lattice Boltzmann equation are described or modeled by addition of a white Gaussian noise source. For stationary states a fluctuation-dissipation theorem relates the variance of the fluctuations to the linearized Boltzmann collision operator and the pair correlation function.

Lattice Boltzmann method is relatively new method in the field of computational fluid dynamics. It has been derived from lattice gas automata and is still under development. Basic steps of the LBM (collision, streaming, boundary conditions, macroscopic quantities) will be presented. Comparison with the finite difference method that uses Navier-Stokes equation on a lid driven cavity benchmark te...

In this chapter, we present a GPU-based implementation of a photon transport model that is particularly effective in global illumination of participating media, including atmospheric geometry such as clouds, smoke, and haze, as well as densely placed, translucent surfaces. The model provides the “perfect” GPU application in the sense that the kernel code can be structured to minimize control fl...

A model for real-time generation of deep-water waves is suggested. It is based on a lattice-Boltzmann (LB) technique. Computation of wave dynamics and (ray-traced) rendering for a lattice of size 1024 can be carried out simultaneously on a single graphics card at 25 frames per second. In addition to the computational speed, the LB technique is seen to offer a simple and physically accurate meth...